Neurodynamics in Randomly Coupled Circle Maps

The dynamics of retrieval processes in a system composed of coupled circle maps is studied by means of a statistical method and numerical simulations. Phase patterns are embedded in coupling parameters so that the system may work as an associative memory system. A parameter, which is an amplification factor multiplied to all the coupling strengths, is introduced for investigating the effect of the strength of the coupling nonlinearity on the behavior of the system concerned. The statistical method provides a set of time evolution equations representing the macroscopic behavior. It is found that the storage capacity is considerably enhanced by the introduced amplification factor. It is also shown that the system exhibits macroscopic chaotic oscillations when the strength of the coupling is sufficiently large. Moreover, the clustering is observed, as in other types of the globally coupled nonlinear systems.